Causality, Modality and Explanation

TL;DR

This paper introduces a sequent calculus for a modal reformulation of nonmonotonic logic, demonstrating cut elimination and arguing that nonmonotonic reasoning is more manageable than traditionally perceived.

Contribution

It develops a new proof system for nonmonotonic logic with cut elimination, reducing complexity and addressing philosophical concerns about nonmonotonic reasoning.

Findings

Proves cut elimination for the system

Shows practical applicability with finitary rules

Critiques philosophical worries about nonmonotonicity

Abstract

We present a sequent calculus system for a modal reformulation of a system of nonmonotonic logic due to McCain and Turner: we prove cut elimination for our system. The proof system is in general infinitary: because we can prove cut elimination, many applications need, in practice, only the application of finitary rules. Consequently, nonmonotonic logic is, in many cases, much less scary than it might seem to be a priori. We derive from this a critique of Fodor's philosophical worries about the nonmonotonicity of human reasoning.